Question 120130
3x - 4y = -1
11y + 2 = 13x
I have to solve this problem using substitution
:
Let's use the 1st equation for substitution in the 2nd equation:
3x - 4y = -1
:
3x = 4y + 1; Added 4y to both sides
:
x = {{{4/3}}}y + {{{1/3}}}; Divided both sides by 3
:
:
Substitute the above for x in the 2nd equation:
11y + 2 = 13x
:
11y + 2 = 13({{{4/3}}}y + {{{1/3}}})
:
11y + 2 = {{{52/3}}} + {{{13/3}}}; multiplied inside the brackets by 13
:
Multiply equation by 3 to get rid of the those annoying denominators
3(11y) + 3(2) = 3*{{{52/3}}}y + 3*{{{13/3}}}
:
33y + 6 = 52y + 13
:
33y - 52y = 13 - 6
:
-19y = +7 
:
y = {{{7/(-19)}}}
:
y = {{{-7/19}}}
:
Find x
x = {{{4/3}}}y + {{{1/3}}};
: 
Substitute {{{-7/19}}} for y
x = {{{(4/3)*(-7/19)}}} + {{{1/3}}}; 
x = {{{-28/57}}} + {{{19/57}}};
x = {{{-9/57}}}
Reduces to:
x = {{{-3/19}}}
:
:
Check solutions in 2nd equation:
11y + 2 = 13x
11({{{-7/19}}}) + 2 = 13({{{-3/19}}})
{{{-77/19}}} + 2 = {{{-39/19}}}
{{{-77/19}}} + {{{38/19}}} = {{{-39/19}}} confirms our solutions
:
This was nasty problem with a lot of steps and fractions;
 but each step by itself, is a simple operation; try following it step-by-step.
Let me know how you do.